So we have this description of gravity as curving space-tim…

There are different lie groups that coorespond to symmetries of different things, so you can have a symmetry of space and that gives you a Lie Group cooresponding to rotations.

That's a 3D lie group.

So for example in 3-Dimensions of space, you can rotate around 3 different axis, 3 different planes.

Other than these towers of Lie Groups, there's 5 out of nowhere exceptional cases that don't seem to be the symmetry of anything but themselves really.

There are Lie Groups for roataions in space, there another set of lie groups for rotations in complex space that can go up to arbitrarily high dimensions, so there's these different infinite collections.

But, mathematically if you work out the classification of all different possible Lie Groups, they stand out as 5 different weird special things.

This is the way it works in all Lie Groups.

There are these very beautiful intricitely intertwined and complex mathematical structures called Lie Groups

That as a combined lie group forms a 6D lie group.

But when you go to into particle physics and you want to describe well how does an electron interact and how does that move and interact gravitationally, its freaking ugly. It's not geometric in the same way the description of gravity is geometric.

When you consider that we're in 4D space-time, then this has 6-Dimensions because as well as the 3-Dimensions of space you can also move in 3 Directions.

There's these 5 Exceptional Lie Groups : G2, F4, E6, E7, and E8; with E8 being the largest and most complicated. It's a 248-Dimensional Lie Group, fundamentally it's not different than the 3D group of rotations of space. It's structure is the same.

Same thing in E8, if you have a different elementary particle cooresponding to each different direction of this 248-Dimensional Lie Group, then when you have rotations along those directions in this Lie Group, that's 2 particles interacting to give a 3rd.

The structure of some of these Lie Groups, which are exceptional cases of Lie Groups, turn out to coorespond to exactly the properties of electrons and other elementary matter particles also intertwined with gravity and all the other forces.

There are different "stacks" for different dimensions of Lie Groups.

These rotations interact - 2 interactions will give a 3rd.

https://arxiv.org/pdf/math/0105155.pdf